Nano-indentation tests to characterize hydraulic fractures

ABSTRACT

A rock sample is nano-indented from a surface of the rock sample to a specified depth less than a thickness of the rock sample. While nano-indenting, multiple depths from the surface to the specified depth and multiple loads applied to the sample are measured. From the multiple loads and the multiple depths, a change in load over a specified depth is determined, using which an energy associated with nano-indenting rock sample is determined. From a Scanning Electron Microscope (SEM) image of the nano-indented rock sample, an indentation volume is determined responsive to nano-indenting, and, using the volume, an energy density is determined. It is determined that the energy density associated with the rock sample is substantially equal to energy density of a portion of a subterranean zone in a hydrocarbon reservoir. In response, the physical properties of the rock sample are assigned to the portion of the subterranean zone.

CROSS-REFERENCE TO RELATED PATENT APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.16/723,610, filed Dec. 20, 2019, which is a continuation of and claimsthe benefit of priority to U.S. Pat. No. 10,520,407, which issued frompatent application Ser. No. 15/909,659, filed Mar. 1, 2018, the contentsof all of which are incorporated by reference herein in their respectiveentirety.

TECHNICAL FIELD

This disclosure relates to analyzing rock formations, for example,hydrocarbon-carrying rock formations.

BACKGROUND

Unconventional reservoirs are generally any reservoir (for example,hydrocarbon-carrying reservoir) in which special recovery operations(that is, recovery operations outside conventional operating practices)are employed. Unconventional reservoirs include reservoirs such astight-gas sands, gas and oil shales, coalbed methane, heavy oil and tarsands, and gas-hydrate deposits, to name a few.

Shale reservoirs, for example, require large hydraulic fracturemultistage design in order to maximize barrel of oil equivalent (BOE)well production. Methods to predict the propagation length, height,location and extent of these networks and their connectivities with bothinherent natural fractures as well as induced micro- and nano-cracks areimportant components of reservoir storativity potentials andproductivity predictions. Microseismic mapping is used to determine thelocation and geometry of the hydraulically fractured reservoir with itsfracture network and connectivity. The fracture network represented bythe microseismic event cloud is then approximated volumetrically inorder to better correlate the network to the well performance. Thisso-called stimulated reservoir volume (SRV), or 3D volume of the createdfracture network, is obtained from mapping of microseismic data and thenrelated to the total volume of injected fluid and the well performance.

SUMMARY

This disclosure describes technologies relating to nano-indentationtests to characterize hydraulic fractures.

Certain aspects of the subject matter described here can be implemented,in a first example implementation, as a method. A rock sample isnano-indented from a surface of the rock sample to a specified depthwithin the rock sample. The specified depth is less than a thickness ofthe rock sample. The rock sample has physical properties. Whilenano-indenting the rock sample, multiple depths from the surface to thespecified depth and multiple loads applied to the sample are measured.Each load is associated with a respective depth. From the multiple loadsand the multiple depths, a change in load over a specified depth isdetermined. From the change in load over a specified depth, an energyassociated with nano-indenting rock sample is determined. From aScanning Electron Microscope (SEM) image of the nano-indented rocksample, an indentation volume is determined responsive to nano-indentingthe rock sample. An energy density associated with the rock sample isdetermined based, in part, on the determined energy and the indentationvolume. It is determined that the energy density associated with therock sample is substantially equal to energy density of a portion of asubterranean zone in a hydrocarbon reservoir. The subterranean zone issubstantially larger than the rock sample. The physical properties ofthe rock sample are assigned to the portion of the subterranean zone inresponse to determining that the energy density associated with the rocksample is substantially equal to the energy density of the portion ofthe subterranean zone.

In an aspect combinable with the first example implementation, thethickness of the rock sample is substantially 1 millimeter. Tonano-indent the rock sample, a nano-indenter can be positioned on thesurface of the rock sample. The surface of the rock sample can bepenetrated using the nano-indenter by a distance that is at least equalto 10 nanometers and less than a thickness of the rock sample.

In another aspect combinable with any of the other aspects, to measurethe multiple depths and the multiple loads, the surface of the rocksample can be penetrated using the nano-indenter to a first of themultiple depths. While doing so, a load applied by the nano-indenter onthe rock sample from the surface to the first depth can be measured.

In another aspect combinable with any of the other aspects, a distal endof the nano-indenter can have a pyramid shape terminating at apenetrating dip. To determine, from the SEM image of the nano-indentedrock sample, and indentation volume, a cross-sectional area of a regionpenetrated by the nano-indenter can be determined. The indentationvolume can be determined based on the cross-sectional area and thespecified depth.

In another aspect combinable with any of the other aspects, a plot ofthe multiple loads versus the multiple depths can be generated. Multipleslopes of the generated plot can be determined. The multiple slopescorrespond to multiple changes of load over specified depth includingthe determined change of load over specified depth.

In another aspect combinable with any of the other aspects, each slopeof the multiple slopes represents a failure of the rock sampleresponsive to the nano-indenting. A failure type can be associated tothe determined change of load over specified depth.

In another aspect combinable with any of the other aspects, an area of aportion of the plot that corresponds to the change in load over at thespecified depth is determined to determine the energy associated withnano-indenting the rock sample from the change in load over thespecified depth.

In another aspect combinable with any of the other aspects, the changein the load can be multiplied by the specified depth to determine theenergy associated with nano-indenting the rock sample from the change inload over the specified depth.

In another aspect combinable with any of the other aspects, the energycan be divided by the indentation volume to determine the energy densityassociated with the rock sample based, in part, on the determined energyand the indentation volume.

Certain aspects of the subject matter described here can be implemented,in a second example implementation, as a method. Energy density of aportion of a subterranean zone in a hydrocarbon reservoir is obtained.An energy density of a rock sample that is substantially smaller thanthe portion of the subterranean zone is determined. To do so, the rocksample is nano-indented to a depth of less than a thickness of thesample. An energy associated with a pop-in case determined. The pop-inrepresents a rate of change of nano-indentation loads over a unit depththat is different from a threshold rate of change of nano-indentationloads over the unit depth. An indentation volume is determinedresponsive to nano-indenting the rock sample. It is determined that theenergy density of the portion of the subterranean zone is substantiallyequal to the determined energy density of the rock sample. Physicalproperties of the rock sample are assigned to the portion of thesubterranean zone in response to determining that the energy density ofthe portion of the subterranean zone is substantially equal to thedetermined energy density of the rock sample.

In another aspect combinable with the second implementation, thethickness of the rock sample is between seven and ten times the depth towhich the rock sample list nano-indented.

In another aspect combinable with any of the other aspects, the energydensity of the portion of the subterranean zone is a first energydensity of the first portion of the subterranean zone. The rock sampleis a first rock sample. The energy density is a first energy density.Multiple energy densities including the first energy density of multipleportions including the first portion of the subterranean zone areobtained. Multiple energy densities including the first rock density ofmultiple rock samples including the first rock sample are determined.Physical properties of each rock sample are assigned to a portion of themultiple portions based on a result of combating the multiple energydensities of the multiple portions with the multiple energy densities ofthe multiple rock samples.

Certain aspects of the subject matter described here can be implemented,in a third example implementation, as a method. Multiplenano-indentation experiments are performed on multiple rock samples.Each nano-indentation experiment includes nano-indenting a rock samplefrom a surface of the rock sample to a specified depth within the rocksample. The specified depth is less than a thickness of the rock sample.Responsive to the multiple nano-indentation experiments, multipleload-depth curves are obtained. Each load-depth curve identifies, foreach rock sample, multiple loads on the rock sample measured duringpenetration from the surface to the specified depth. From the multipleload-depth curves, multiple pop-ins experienced by the multiple rocksamples are determined. Each pop-in is associated with respect tosample. Each pop-in represents a rate of change of loads over a unitdepth that this different from a threshold rate of change of loads overthe unit depth. Multiple energies associated with the multiple pop-insare determined. Each energy is released in response to a correspondingpop-in in that aspect of sample. For the multiple rock samples, acorresponding multiple nano-indentation volumes are determined. Eachnano-indentation volume represents a volume of the rock sample indentedresponsive to a corresponding nano-indentation experiment. Multipleenergy densities are determined for the multiple rock samples, from themultiple energies, and the multiple nano-indentation volumes. Physicalproperties of one or more of the rock samples are assigned to one ormore portions of a subterranean zone based on a result of combating themultiple energy densities for the multiple rock samples with multipleenergy densities of corresponding multiple portions of the subterraneanzone.

In another aspect combinable with the third example implementation, eachenergy of the multiple energies is classified as belonging to one ofthree categories of energies to determine to multiple energiesassociated with the multiple pop-ins.

In another aspect combinable with any of the previous aspects, thethickness of each rock sample can be between seven and ten times thedepth to which the rock sample is nano-indented.

The details of one or more implementations of the subject matterdescribed in this specification are set forth in the accompanyingdrawings and the description that follows. Other features, aspects, andadvantages of the subject matter will become apparent from thedescription, the drawings, and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A-1C are schematic diagrams of performing nano-indentingexperiments on rock samples.

FIG. 2 is a flowchart of an example process to determine fracturedimensions and stimulated reservoir volumes based on the nano-indentingexperiments on rock samples.

FIGS. 3A and 3B are schematic diagrams of nano-indenting rock samples indirections perpendicular and parallel to the bedding planes.

FIGS. 4A-4C are schematic diagrams of three different types of pop-ins.

FIG. 5 is a flowchart of an example process of determining physicalproperties of a subterranean zone based on nano-indenting experiments onrock samples.

Like reference numbers and designations in the various drawings indicatelike elements.

DETAILED DESCRIPTION

Fracture mapping via micro-seismic activity can be unreliable. Thisdisclosure describes techniques to determine the types of shale or rockmechanical failures associated with specific nano- and micro-seismicevents. Implementations of the techniques described here can enable abetter understanding of the failures associated with sonic recordingsand, in turn, enable a better description of the location and geometryof the associated rock or shale micro-fractures compared to existingtechniques to do the same. As described in more detail later, thetechniques involve identifying pop-ins in nano-indentationload-displacement curves obtained by performing nano-indentationexperiments (or tests or operations) on multiple rock samples, forexample, shale or other rock sample obtained from unconventionalreservoirs.

Pop-ins are localized failures observed in nano-indentationload-displacement curves where a sudden burst of relatively largedisplacement occurs at a relatively constant force value. In sourceshales, a multi-phase natural porous material with polymeric organiccomponents, the occurrence of pop-ins has a basis in micromechanics andthe failure of granular cohesive-frictional material. Analysis ofpop-ins in shale by high resolution scanning electron microscopy (SEM)images has shown that each pop-in or the consecutive series of pop-insare the result of local brittle or abrupt failure of individualcomponents, such as a silicate grain crushed under a nano-indenter tipor instantaneous planes of slippage between grains, or localized shearfailures. In addition, the shear band deformations in a single loadingstreak form brittle-ductile couplets, thus creating a small burst ofenergy, (for example, nano-Joules (nJ) of energy), at constant loadsalso called pop-ins, or, in energy terms, as “sudden energy burstintensity” (SEBI). The tremendous forces exerted by the nano-indenter atthese nano- and micro-volume scales trigger local rock failures similarin nature and failure mechanics to tectonic forces and hydraulicfracture energy triggered in fault generation, hydraulic fracturing, andinduced micro- and macro-seismic events.

This disclosure describes correlating nano or micro-energy dissipationassociated with indentations with micro-scale volume imprints todiscrete shale failure events that could be identical to fieldmacro-scale events registered sonically. Each failure type (for example,crack initiation, catastrophic failure, shearing, abrupt shale or facesdislocation, to name a few) is captured as a nano- or micro-seismicevent or activity. Each type of event and its intensity range(correlated to failure mechanism) is established and used to fingerprintthe location of the failure, its type, and its associated energy. Theinformation is assimilated for identifying the hydraulic fracturingnetwork extension related to the micro-seismic events relevant tohydraulic fracture propagation azimuth and dimensions associated withthe SRV concept.

In this manner, the techniques provide improved characterization of thehydraulic fracturing extension and dimensions created duringstimulation. The technique utilizes not only the energy and location ofmicro-seismic events to determine potential hydraulic fracture extensionand dimensions, but also incorporates the type and extent of failureassociated with such events. The technique correlates geo-mechanicalinterpretations of reservoir source shale failures with geophysical datavis-à-vis energy density at failure, that is, SEBI. The technique is acost-effective technique for improving estimated SRV models thatutilizes existing laboratory resources and micro-seismic data bycharacterizing the micro-failures correlated to energy density inequivalent volume of shale or rock that has failed.

FIGS. 1A-1C are schematic diagrams of performing nano-indentingexperiments on rock samples. FIG. 1A is a schematic diagram of anano-indentation experimentation system (for example, a NanoTest VantageSystem™ offered by Micro Materials Limited, Wrexham, UK) performed on arock sample 102. Example techniques implemented using the systemschematically shown in FIGS. 1A-1C are described later.

In some implementations, the rock sample 102 can be a micro-scale rocksample having a thickness in the micrometer range (that is, less than orequal to 1 cm). The upper limit for thickness allows correlating thedepth of the test with sample properties being tested at the depth. Therock sample 102 can be obtained from an unconventional reservoir inwhich hydrocarbons (for example, oil, gas, combinations of them) areentrapped. For example, the rock sample 102 can be a shale sampleobtained from a shale reservoir. The rock sample 102 can have certainphysical properties, for example, hardness, fracture toughness, elasticmoduli, to name a few.

The rock sample 102 can be positioned adjacent to a nano-indenter 104 tonano-indent the sample. For example, the nano-indenter 104 can be aBerkovich indenter with a tip contact area that has been calibrated byindenting into fused silica. Alternatively, the indenter can have aspherical, cono-spherical, cube corner or other geometry.

The system includes a computer system 106 that is operably connected tothe nano-indenter 104 and configured to control the nano-indenter 104 toperform operations, for example, nano-indenting the rock sample 102. Insome implementations, the computer system 106 can include acomputer-readable medium 106 a storing computer instructions executableby one or more processors 106 a to perform operations including, forexample, transmitting instructions to the nano-indenter 104 to performnano-indenting operations on the rock sample 102 and to receive signalsrepresenting results of the nano-indenting operations. The computersystem 106 can be connected to input devices (not shown) using which auser can provide instructions, and output devices (for example, adisplay device 108) on which the computer system 106 can display resultsof the nano-indenting operations.

For example, the computer system 106 can measure load-displacementcurves (for example, the curve 110) responsive to the nano-indentationoperations and display the curves in the display device 108. Aload-displacement curve shows displacement on the X-axis and load on theY-axis. The displacement is a depth by which the nano-indenter 104indents the surface of the rock sample 102. The load is thecorresponding load on the nano-indenter 104 to indent to that depth. Ingeneral, the depth to which the nano-indenter 104 indents is betweenseven and ten times the thickness of the rock sample. As describedlater, pop-ins can be observed in the load-displacement curves.

In FIG. 1A, the computer system 106 is schematically shown to beseparate from the nano-indenter 104. In such implementations, thecomputer system 106 can be a desktop computer, a laptop computer, atablet computer, a smartphone or other computer system. In someimplementations, the nano-indenter 104 and the computer system 106 canbe included in the same physical structure. Such a physical structurecan also include the display device 110.

FIG. 1B is a schematic diagram of an imaging system 112 to imagenano-indentations on the rock sample 102. In some implementations, theimaging system 112 can include a Scanning Electron Microscope (SEM).Alternatively, or in addition, the imaging system 112 can include anAtomic Force Microscope (AFM) or an optical microscope. In general, theimaging system 112 can obtain images at sufficient resolution to be ableto see individual indentations and the residual impression left in therock sample 102. For example, FIG. 1B shows the rock sample 102 havingfour nano-indentations (nano-indentations 114 a, 114 b, 114 c and 114d). Each nano-indentation is made by the same nano-indenter. Thedifference in the sizes and shapes of the nano-indentations is due tothe difference in the depths to which the nano-indenter 104 penetratedthe surface of the rock sample 102. In some implementations, the rocksample 102 can be positioned within the imaging system 112 afternano-indentation by the nano-indenter 104. Alternatively, thenano-indenter 104 can be positioned within the imaging system 112 suchthat not only the indentations and residual impression but thenano-indentation experiments themselves can also be imaged using theimaging system 112.

FIG. 1C is a schematic diagram of the computer system 106. The computersystem 106 can receive, as input, the nano-indentation images capturedby the imaging system 112. The computer system 106 can additionallyreceive, as input, energy density of a portion of a subterranean zone.The subterranean zone can be a formation, a portion of a formation ormultiple formations. The physical properties of the reservoir rock canvary across a depth of the subterranean zone from a surface of theEarth. Energy densities at different depths in the subterranean zone canbe measured and provided to the computer system 106 as input. Forexample, the energy densities can be stored on a computer storage medium116. Based on the nano-indentation images received from the imagingsystem 112, the computer system 106 can determine an energy density forthe rock sample 102. The computer system 106 can compare the energydensity for the rock sample 102 with the energy densities of thedifferent portions of the subterranean zone. Based on results of thecomparison, the computer system 106 can identify a portion of thesubterranean zone whose energy density matches that of the rock sample102. In response, the computer system 106 can assign physical propertiesof the rock sample 102 to the rock in the portion of the subterraneanzone. For example, the computer system 106 can output the physicalproperties which can be stored on the computer storage medium 116. Bydoing so, the computer system 106 can predictively determine physicalproperties of the subterranean zone using energy densities of rocksamples determined from nano-indentation tests.

FIG. 2 is a flowchart of an example process 200 to determine fracturedimensions and stimulated reservoir volumes based on the nano-indentingexperiments on rock samples. The process 200 can be implemented by thesystem schematically identified in and described with reference to FIGS.1A-1C. At 202, core samples are obtained from a subterranean zone (forexample, a reservoir such as an unconventional hydrocarbon reservoir).The core samples (for example, shale core samples) can be obtained fromthe reservoir before hydraulic fracture stimulation. In someimplementations, one or more rock samples (for example, like the rocksample 102) can be prepared from the core samples. To do so, each coresample can be mechanically cut and polished to create rock samples, eachhaving a substantially flat indentation surface and a thickness ofsubstantially 1 millimeter (mm). In general, a rock sample can be cutand polished to a thickness that can allow performing as much as severalhundred nano-indentations without traversing the thickness of thesample. FIGS. 3A and 3B are schematic diagrams of nano-indenting rocksamples in directions perpendicular and parallel to the bedding planes.One or more of the rock samples (for example, rock sample 304 in FIG.3A) can be cut and polished such that the indentation surface isparallel to the bedding plane of the sample and nano-indentation will beperpendicular to the bedding plane. Other rock samples (for example,rock sample 306 in FIG. 3B) can be cut and polished such that theindentation surface is perpendicular to the bedding plane of the sampleand nano-indentation will be parallel to the bedding plane of thesample.

At 204, indentation and imaging can be performed one or more times oneach rock sample. For each nano-indentation, the nano-indenter 104 canbe penetrated from the indentation surface of the rock sample to aspecified depth within the sample. The specified depth is less than athickness of the sample. While nano-indenting the rock sample, thecomputer system 106 (or both) can measure multiple depths from thesurface to the specified depth and multiple loads applied to the sample.Each load is associated with a respective depth. From the measureddepths and loads, the computer system 106 (or both) can developload-displacement curves for each nano-indentation. For example, one ormore (or all) of nano-indentation experiments can involve applying loadsranging from 1 milli Newton (mN) to 400 mN to depths ranging from 100nanometer (nm) to 7,000 nm.

A subset of (that is, one or more or all of) the rock samples mayexhibit pop-ins, which are characterized by a sudden increase indisplacement with or without a necessary change in force on theload-displacement curve. Pop-ins can appear immediately and frequentlythroughout source shale nano-indentation testing. In many cases, thefirst burst is not unique in a single load-displacement curve cycle butrather is followed by additional sudden bursts. For example, pop-ins canbe seen in the load displacement curve 108 (FIG. 1A) was developed fromtest data containing two sets of 10 indentations performed on shalesamples at a maximum load of 100 mN. A pop-in can be characterized bycatastrophic failures such as grain crushing, grain pile-ups, multilayerpile-ups and grain punching into softer layers. In some instances, arock sample may not exhibit any pop-in. Such samples are ignored in theanalysis described in this disclosure.

At 206, failure types associated with respective pop-ins can bedetermined and classified. For each load-displacement curve, thecomputer system 106 can be configured to determine a change in load (p)over a specified depth (h) to identify a slope, that is, a gradient offorce over displacement (Δp/Δh), from which pop-ins can be observed ordetermined. FIGS. 4A-4C are schematic diagrams of three different typesof pop-ins, each corresponding to a different failure mechanism. FIG. 4Ashows a Type I pop-in in which the load-displacement curve exhibits adiscontinuity at a constant force. Thus, the gradient of force overdisplacement, that is, Δp/Δh, is zero. A Type I pop-in falls between twonearly elastic responses on the load-displacement curve when thenano-indentation direction is perpendicular to the bedding plane (sample302, FIG. 3A). That is, after the Type I pop-in, a linear elasticdeformation took place before the onset of a Type II pop-in. FIG. 4Bshows a Type II pop-in defined by a sudden displacement in theload-displacement curve where the slope (Δp/Δh) is greater than zero.FIG. 4C shows a Type III pop-in defined by a sudden displacement in theload-displacement curve where the slope (Δp/Δh) is less than zero.

To determine pop-ins, the computer system 106 can store loads andcorresponding displacements for each nano-indentation experiment in acomputer-readable medium (for example, the computer-readable medium 106b or separate computer storage medium). To determine a change in load,the computer system 106 can determine a difference of a stored loadvalue and a stored preceding load value. The two values can beconsecutive (that is, with no intermediate load values) or can besuccessive (that is, with intermediate load values). Similarly, todetermine a change in displacement, the computer system 106 candetermine a difference of a stored displacement value and a storedpreceding displacement value, which can be consecutive or successive. Todetermine a pop-in, the computer system 106 can determine a slope bydividing the change in load by the change in slope. The computer system106 can determine if the slope is zero, greater than zero or less thanzero, and, based on the result, classify a pop-in as Type I, Type II orType III, respectively. In sum, for each load-displacement curve in anano-indentation experiment, the computer system 106 can store thenumber of pop-ins and the type of each pop-in. In alternative oradditional implementations, pop-ins can be observed and determinedmanually using the load-displacement curves.

A single load-displacement curve measurement can yield multiple pop-ins.For example, as described earlier, multiple pop-ins can be seen in theload displacement curve 108 (FIG. 1A) was developed from test datacontaining two sets of 10 indentations performed on shale samples at amaximum load of 100 mN. Moreover, multiple load-displacement curves canbe generated for the same rock sample. Depending on the area of theindentation surface, multiple nano-indentation experiments can beperformed at multiple, different locations on the rock sample. Forexample, FIG. 1B shows four nano-indentation experiments performed onthe rock sample 102. In addition, multiple rock samples can be formedfrom the same core sample and subjected to the nano-indentationexperiments. Thus, the computer system 106 can identify multiple pop-insfor rock obtained from a particular portion of the subterranean zone.

As described earlier, in source shales, a multi-phase natural porousmaterial with polymeric organic components, the occurrence of pop-inshas a basis in micromechanics and the failure of granularcohesive-frictional material. In other words, a pop-in is representativeof physical properties of the rock sample. The physical properties ofthe rock obtained from the particular portion of the subterranean zonecan be determined using known techniques. In addition, thenano-indentation techniques described here can be used to determine thephysical properties of individual rock samples. The computer system 106can correlate pop-ins observed or determined for rock obtained from aparticular portion of the subterranean zone to the physical propertiesof the rock obtained from that portion of the subterranean zone. Asdescribed later, the computer system 106 can develop the correlationusing energy densities associated with the rock.

As described earlier, an imaging system 112 (for example, a SEM or AFM)can be used to image the nano-indentations and to provide the images tothe computer system 106. The computer system 106 can determine energydensities for a rock sample using the images and using the one or moreload-displacement curves measured for that sample. Energy density, inthis context, refers to the energy required, for example, to fracturethe rock during nano-indentation of the rock sample. Energy density alsorefers, on a comparatively larger scale, to microseismic energydensities detected in observation wells by geosensors or acousticsensors. To determine the energy for Type I pop-ins, the load at whichthe pop-in occurs is multiplied by the total displacement of theindenter over the span of the pop-in (that is, the final depth− theinitial depth). To determine the energy for Type II pop-ins, the averageload at which the pop-in occurs (that is, (final load−initial load)/2)is multiplied by the total displacement of the indenter over the span ofthe pop-in (that is, final depth−initial depth). Approximately 70% ofthe pop-in events dissipated less than 7 nano Joules (nJ) of energywhile less than 5% of the pop-ins produced more than 40 nJ of energy.Pop-ins occur across a wide range of depths or loads or both.

Energy density, then, is the energy to fracture the rock per unit volumeof the rock. In some implementations, energy density of a rock sample isdetermined by dividing the energy to fracture the rock sample by thevolume of indented rock sample. In some implementations, the volume ofthe indented rock sample can be determined by measuring the residualshape left by the nano-indenter on the surface of the rock sample usingthe imaging system 112, and performing geometric calculations. Forexample, if the tip of the nano-indenter 104 is shaped like a pyramid,then the residual shape left by the nano-indenter on the surface of therock sample can be approximated to be rectangular. Tips of othernano-indenters with other shapes can leave correspondingly differentresidual shapes on the rock sample surface. The volume of the indentedrock sample can then be determined by multiplying the residual shape bythe depth of indentation. In some implementations, the computer system106 can be configured to implement image analysis techniques todetermine the dimensions of the residual shape, determine an area of theresidual shape from the dimensions and multiply the area by thenano-indentation depth that is, for example, stored in thecomputer-readable medium. Alternatively, the dimensions or the area orthe volume (or any combination of them) can be manually calculated, forexample, by a user, and provided to the computer system 106 as an input.The computer system 106 can be configured to determine the energydensity for the rock sample by implementing the techniques describedearlier.

At 208, field micro-seismic data are obtained on hydraulic fracturepropagation. For example, the micro-seismic data are obtained viageophones by receiving an acoustic wave signal transmitted by localizedfractures shearing (thus sending an acoustic signal) due to thepropagation of the main hydraulic fracture in the subterranean zone. Thevolume of the hydraulically fractured subterranean zone, can bedetermined from the decibel levels of individual microseismic signalscollected as the HF propagates. For example, the acoustic wave can betransmitted through a fracture that is about 100 feet high and about1,000 feet long, and the response can be evaluated to determine theenergy density.

At 210, micro-seismic event moments and energy magnitudes are obtained.Microseismic monitoring typically results in capturing the location ofevents and the magnitude or strength (or both) of the events. Momentmagnitude is used to describe a microseismic event. Moment magnituderelates to the distance the rock moves along a fault or fracture and thearea of the fault or surface of the fracture. The moment magnitude isthe amount of energy released by the event.

At 212, seismic energy obtained from the field (by implementing step210) is correlated with energy density determined from thenano-indentation experiments. To do so, for example, the computer system106 can match field-level energy density values for a portion of asubterranean zone to energy density values determined for the rocksamples.

At 214, a type of failure associated with the seismic events can bedetermined. For example, upon determining that an energy density valuedetermined for a rock sample matches a field-level energy density valuefor a portion of the subterranean zone, the computer system 106 canassociate pop-ins determined for the rock sample to the portion of thesubterranean zone. The association is a prediction that rock in theportion of the subterranean zone will exhibit the same or substantiallyidentical types of failures as that exhibited by the rock sample.Accordingly, the computer system 106 can assign the physical propertiesdetermined for the rock sample to the portion of the subterranean zone.In this manner, the physical properties of the portion of thesubterranean zone can be predictively determined.

At 216, fracture dimensions and SRV can be determined. The stimulatedreservoir volume (SRV) is an estimate of the volume of the openfractures which are contributing to the flow of hydrocarbons to thewell. The microseismic data which includes the location and magnitude offailure events provides an overall picture of the fractured formation.

FIG. 5 is a flowchart of an example process 500 of determining physicalproperties of a subterranean zone based on nano-indenting experiments onrock samples. The process 500 can be implemented either entirely or inpart using the system described with reference to FIGS. 1A-1C. At 502, arock sample is nano-indented from a surface of the rock sample to aspecified depth within the rock sample. At 504, while nano-indenting therock sample, multiple depths from the surface to the specified depth andmultiple loads applied to the sample are measured, each load associatedwith a respective depth. At 506, a change in load over a specified depthis determined from the multiple loads and multiple depths. At 508, anindentation volume is determined from an image (for example, a SEM imageor an AFM image) of the nano-indented sample. At 510, an energy densityassociated with the rock sample is determined based, in part, on thedetermined energy and the indentation volume. At 512, the energy densityis compared with energy density of a portion of a subterranean zone. Itis determined that the energy density associated with the rock sample issubstantially equal to energy density of a portion of a subterraneanzone in a hydrocarbon reservoir. The subterranean zone is substantiallylarger than the rock sample. At 514, the physical properties of the rocksample are assigned to the portion of the subterranean zone in responseto determining that the energy density associated with the rock sampleis substantially equal to energy density of a portion of a subterraneanzone in a hydrocarbon reservoir. At 516, it is determined if anotherrock sample is available to be nano-indented. Alternatively or inaddition, it can be determined if the same rock sample is to be furthernano-indented. If yes, then the process 500 is repeated starting at step502. If no, then the process 500 ends.

Thus, particular implementations of the subject matter have beendescribed. Other implementations are within the scope of the followingclaims.

The invention claimed is:
 1. A method comprising: positioning a rocksample within a Scanning Electron Microscope (SEM); within the SEM,nano-indenting the rock sample from a surface of the rock sample to aspecified depth within the rock sample, the specified depth less than athickness of the rock sample; imaging, using the SEM, nano-indenting therock sample from the surface of the rock sample to the specified depthwithin the rock sample; while nano-indenting the rock sample, measuringa plurality of depths from the surface to the specified depth and aplurality of loads applied to the sample, each load associated with arespective depth; determining, from the plurality of loads and theplurality of depths, a change in load over a specified depth;determining, from the change in load over a specified depth, an energyassociated with nano-indenting the rock sample; determining, from a SEMimage of the nano-indented rock sample, an indentation volume responsiveto nano-indenting the rock sample; and determining an energy densityassociated with the rock sample based, in part, on the determined energyand the indentation volume.
 2. The method of claim 1, further comprisingimaging, using the SEM, nano-indenting the rock sample from the surfaceof the rock sample to the specified depth within the rock sample.
 3. Themethod of claim 1, wherein the thickness of the rock sample issubstantially 1 millimeter, and wherein nano-indenting the rock samplecomprises: positioning a nano-indenter on the surface of the rocksample; and penetrating the surface of the rock sample using thenano-indenter by a distance that is at least equal to 10 nanometers andless than a thickness of the rock sample.
 4. The method of claim 1,further comprising: penetrating the surface of the rock sample using thenano-indenter by the distance to a depth; and while penetrating thesurface of the rock sample to the depth, measuring a load applied by thenano-indenter on the rock sample from the surface to the depth.
 5. Themethod of claim 1, further comprising: performing, using thenano-indenter and within the SEM, a nano-indentation experiment; anddetermining a physical property of the rock sample based on a result ofthe nano-indentation experiment.
 6. The method of claim 1, wherein thethickness of each rock sample is between seven and ten times a depth towhich the rock sample is nano-indented.
 7. The method of claim 1,further comprising: generating a plot of the plurality of loads versusthe plurality of depths; and determining a plurality of slopes of thegenerated plot corresponding to a plurality of changes of load overspecified depth, the plurality of changes of load over specified depthincluding the determined change of load over specified depth.
 8. Themethod of claim 7, wherein each slope of the plurality of slopesrepresents a failure of the rock sample responsive to thenano-indenting, wherein the method further comprises associating afailure type to the determined change of load over specified depth. 9.The method of claim 7, wherein determining, from the change in load overthe specified depth, the energy associated with nano-indenting the rocksample comprises determining an area of a portion of the plot thatcorresponds to the change in load over the specified depth.
 10. Themethod of claim 9, wherein determining, from the change in load over thespecified depth, the energy associated with nano-indenting the rocksample comprises multiplying the change in the load by the specifieddepth.
 11. The method of claim 10, wherein determining the energydensity associated with the rock sample based, in part, on thedetermined energy and the indentation volume comprises dividing theenergy by the indentation volume.
 12. The method of claim 1, wherein,while nano-indenting the rock sample, measuring a plurality of depthsfrom the surface to the specified depth and a plurality of loads appliedto the sample, each load associated with a respective depth comprises:penetrating the surface of the rock sample using the nano-indenter bythe distance to a first depth of the plurality of depths; and whilepenetrating the surface of the rock sample to the first depth, measuringa load applied by the nano-indenter on the rock sample from the surfaceto the first depth.
 13. The method of claim 1, wherein a distal end ofthe nano-indenter has a pyramid shape terminating at a penetrating tip,wherein determining, from the SEM image of the nano-indented rocksample, an indentation volume responsive to nano-indenting the rocksample comprises: determining, from the SEM image, a cross-sectionalarea of a region penetrated by the nano-indenter; and determining theindentation volume based on the cross-sectional area and the specifieddepth.
 14. A method comprising: nano-indenting a rock sample to a depthless than a thickness of the sample while the rock sample is within aScanning Electron Microscope (SEM); imaging nano-indenting the rocksample while nano-indenting the rock sample; determining an energyassociated with a pop-in representing a rate of change ofnano-indentation loads over a unit depth that is different from athreshold rate of change of nano-indentation loads over the unit depth;determining an indentation volume responsive to nano-indenting the rocksample; and determining an energy density of a rock sample based on theenergy and the indentation volume.
 15. The method of claim 14, whereinthe thickness of the rock sample is between seven and ten times thedepth to which the rock sample is nano-indented.
 16. The method of claim14, wherein the thickness of the rock sample is substantially 1millimeter, and wherein nano-indenting the rock sample comprises:positioning a nano-indenter on the surface of the rock sample; andpenetrating the surface of the rock sample using the nano-indenter by adistance that is at least equal to 10 nanometers and less than athickness of the rock sample.